Analog filters play a very important role in communication systems and, more generally, in any analog signal processing system. Since any realizable filter transfer function can be decomposed in a factor of second order sections and first order sections, a very important building block is a second order filter that permits the implementation of complex filter poles. The emphasis in filter design is to implement such second order transfer functions with minimal power dissipation, at low supply voltage, while still maintaining tuning capability and a certain required linearity. In particular, gmC filters, which are based on transconductance amplifiers (gm) working on capacitive loads (C), have very good characteristics at high signal frequencies and are widely used in RF communication systems.
One exemplary second order filter implementation is shown in FIG. 1. An equivalent circuit targeting low voltage supply applications is further shown in FIG. 2. In the above circuit diagrams, the high efficiency comes from the use of a simple MOS device as a transconductance element. Very good high frequency performance is achieved by the lack of intermediate nodes with associated parasitic poles.
An analysis of the equivalent small signal circuit illustrated in FIG. 3 indicates a second order transfer function, if gm1=gm2=gm3,
                                          V            out                                V            in                          =                  1                      1            +                                          sC                1                                            g                m                                      +                                                            s                  2                                ⁢                                  C                  1                                ⁢                                  C                  2                                                            g                m                2                                                                        (        1        )            where: M201, M202, M203, and M204 are assumed matched and having a common transconductance value gm;C1=C221/2;C2=C222/2.
Depending on the relative values of C1 and C2, the second order transfer function in Equation (1) may have a real pole or complex conjugate poles. This choice is made possible by the positive feedback of devices M211 and M212.
The circuits in FIG. 1 and FIG. 2 appear to have two main drawbacks, which the present invention tries to address in detail in several embodiments described below. First, the transfer characteristic and the pole location depend on the transconductance of simple MOS devices. This transconductance value is hard to control over process and especially over temperature. For the circuit in FIG. 2, it is especially difficult to ensure that M211 and M212 devices have the same transconductance as the M201 and M202 devices. If the transconductance values do not match, the circuit may latch up due to positive feedback at low frequencies. On the other hand, if the M211 and M212 have a transconductance intentionally lower than M201 and M202 transconductance, the complex poles are harder to achieve and control.
A second drawback appears to be that the signal linear range is limited by the gate-to-source overdrive. The transconductance is highly non-linear due to the simple MOS devices used and the input and output signals occur directly across the gate to source pins of these MOS devices. If the bias currents are used to adjust the transconductance values over process corner variations (for pole location tuning), this has a compounding effect on limiting the signal linear range. A process fast corner, for example, requires less bias current for a given required transconductance, which means even less gate-to-source overdrive voltage and equivalent reduced linear range. On the slow process corner, the higher bias current required and related larger voltage drops may be limited by power supply level.
It is desirable, therefore, to provide an efficient second order gmC filter implementation without the aforementioned drawbacks.